February 16, 2012

Ergodicity in the frontier of branching Brownian motion

Nicola Kistler, University of Bonn

I will discuss recent results obtained in collaboration with A. Bovier (Bonn) and L.-P. Arguin (Montreal) on the properties of the extremal particles of branching Brownian motion. In particular, I will sketch the main steps in the proof of a conjecture by S. Lalley and T. Sellke [Ann. Probab. 1987] concerning the ergodicity of the frontier.

March 1, 2012

Connectivity of Bluetooth graphs

Nicolas Fraiman, McGill University

We study the connectivity of Bluetooth graphs, these are subgraphs of the random geometric graph model. There are two parameters that control the model: the radius r that determines the visible neighbors of each node, and the number of edges c that each node is allowed to have. The randomness comes from the distribution of nodes in space and the choices of each vertex. We characterize the connectivity threshold (in c) for values of r close the critical value for connectivity in the underlying random geometric graph. This is joint work with Nicolas Broutin, Luc Devroye and Gabor Lugosi.

March 15, 2012

The scaling limit of a partial match process

Nicolas Broutin, INRIA Rocquencourt

We consider the problem of recovering items matching a partially specified pattern in a structure storing data points from the unit square. We assume the traditional model where the data consist of uniform points. For this model, in a structure on n points, it is known that the number of nodes of the structure C_n(U) to visit in order to report the items matching an independent and uniformly random query U in [0,1] satisfies E[C_n(U)] ~ kappa*n^{beta}, where kappa and beta are explicit constants. We develop an approach based on the analysis of the cost C_n(x) of any fixed query x in [0,1], and give precise estimates for the variance and limit distribution of the cost C_n(x). Our results permit to describe a limit process for the costs C_n(x) as x varies in [0,1]; one of the consequences is that E[max_{x in [0,1]} C_n(x)] ~ gamma * n^beta. This is joint work with Ralph Neininger and Henning Sulzbach.

March 29, 2012

To be confirmed

Daniel Remenik, University of Toronto

April 5, 2012

Continuum limits of spiked random matrices

Alex Bloemendal, Harvard University

The top eigenvalues of finite rank perturbations of large Wigner and sample covariance matrices are known to exhibit a phase transition. I will describe joint work with Bálint Virág in which we identify a limiting object near the transition, solving an outstanding problem in the real case. The resulting deformations of the Tracy-Widom distributions can be characterized in terms of the ground state energy of a random Schrödinger operator, a hitting probability of a modified Dyson's Brownian motion, and a special solution of a linear PDE. The PDE turns out to have a surprising connection with some known integrable structure in the complex case; it also appears to be effective for numerical evaluation.

April 12, 2012

Alexander Fribergh, Courant Institute NYU

•  4:30-5:30pm at: McGill in Burnside Hall, room 920